I have a printed map of a district with several points on it that can be used as geo-location reference points.

I have the shapefile of this map in QGIS.
If someone draws a point on the printed map, how can I find the position of the drawn point without scanning the printed map ? 

I was thinking of measuring the distance from that point to three other points on the paper, so I can have the zoom used and find the position. Is there a plugin to help with that? Are there other ways to accomplish this?

Thanks